{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_nums = [-15,-10,-9,-7,-3,0,1,2,3,11,12,18]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#调库排序\n",
    "def algorithm1(nums):\n",
    "    return sorted(num * num for num in nums)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#双指针——正负交叉排序（指针从0分界点开始，分别向左右移动）\n",
    "def algorithm2(nums):\n",
    "    n = len(nums)\n",
    "    negative = -1\n",
    "    for i, num in enumerate(nums):  \n",
    "        if num < 0:\n",
    "            negative = i\n",
    "        else:\n",
    "            break            #负数计数\n",
    "    ans = list()\n",
    "    i, j = negative, negative + 1    #i代表最后一个负数的索引，j代表0的索引\n",
    "    \n",
    "    move = []   #可视化变量\n",
    "    \n",
    "    #使用交叉排序，比较0左右绝对值大小\n",
    "    while i >= 0 or j < n:         #i之前负数平方后递减，所以i从右往左取值，到i=0终止；j之后是非负数，到序列最后n\n",
    "        #先要判断溢出\n",
    "        move.append((i, j))\n",
    "        if i < 0:\n",
    "            ans.append(nums[j] * nums[j])\n",
    "            j += 1\n",
    "        #正数超出部分\n",
    "        elif j == n:\n",
    "            ans.append(nums[i] * nums[i])\n",
    "            i -= 1\n",
    "        #负数超出部分\n",
    "        \n",
    "        #再比较正负两边平方数大小，小的放在序列前一个\n",
    "        elif nums[i]*nums[i] < nums[j]*nums[j]:\n",
    "            ans.append(nums[i]*nums[i])\n",
    "            i -=1                  #取负数向左一个\n",
    "        elif nums[i]*nums[i] >= nums[j]*nums[j]:\n",
    "            ans.append(nums[j]*nums[j])\n",
    "            j +=1                  #取正数向右一个\n",
    "\n",
    "    return ans, move"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#双指针——夹逼排序\n",
    "def algorithm3(nums):\n",
    "    n = len(nums)\n",
    "    ans = [0] * n    \n",
    "    i, j, pos = 0, n - 1, n - 1   #i从第一个元素开始， j从最后一个元素开始\n",
    "    \n",
    "    move = []   #可视化变量\n",
    "    \n",
    "    while i <= j:      #终止条件，指针相遇，从大往小排序\n",
    "        move.append((i,j))\n",
    "        if nums[i] * nums[i] > nums[j] * nums[j]:\n",
    "            ans[pos] = nums[i] * nums[i]\n",
    "            i += 1\n",
    "        else:\n",
    "            ans[pos] = nums[j] * nums[j]\n",
    "            j -= 1\n",
    "        pos -= 1   \n",
    "    return ans, move"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#指针移动可视化\n",
    "def visualize_pointer_movement_with_squares(nums, algorithm):\n",
    "    original_nums = nums.copy()\n",
    "    _, pointer_movements = algorithm(nums.copy())\n",
    "    fig, ax = plt.subplots(figsize=(12, 4))\n",
    "    \n",
    "    for i, num in enumerate(original_nums):\n",
    "        ax.text(i, 0.5, num, ha='center', va='center', fontsize=12)\n",
    "        ax.add_patch(plt.Rectangle((i - 0.5, 0), 1, 1, fill=None, edgecolor='black'))\n",
    "\n",
    "    fast_pointer, = ax.plot([], [], 'r^', label='Fast Pointer', markersize=10)\n",
    "    slow_pointer, = ax.plot([], [], 'bv', label='Slow Pointer', markersize=10)\n",
    "    ax.set_xlim(-0.5, len(nums) - 0.5)\n",
    "    ax.set_ylim(-1, 2)\n",
    "    ax.axis('off')\n",
    "    ax.legend(loc='upper right')\n",
    "\n",
    "    def update(frame):\n",
    "        fast, slow = pointer_movements[frame]\n",
    "        fast_pointer.set_data((fast ,), (1.5,))\n",
    "        slow_pointer.set_data((slow ,), (-0.5,))\n",
    "        return fast_pointer, slow_pointer\n",
    "\n",
    "    ani = animation.FuncAnimation(fig, update, frames=len(pointer_movements), interval=800, blit=True)\n",
    "    return HTML(ani.to_jshtml())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_imgc4bec7bf370947c88ccabfa08cfe9c79\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_sliderc4bec7bf370947c88ccabfa08cfe9c79\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"animc4bec7bf370947c88ccabfa08cfe9c79.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" onclick=\"animc4bec7bf370947c88ccabfa08cfe9c79.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" onclick=\"animc4bec7bf370947c88ccabfa08cfe9c79.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" onclick=\"animc4bec7bf370947c88ccabfa08cfe9c79.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" onclick=\"animc4bec7bf370947c88ccabfa08cfe9c79.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" onclick=\"animc4bec7bf370947c88ccabfa08cfe9c79.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" onclick=\"animc4bec7bf370947c88ccabfa08cfe9c79.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" onclick=\"animc4bec7bf370947c88ccabfa08cfe9c79.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" onclick=\"animc4bec7bf370947c88ccabfa08cfe9c79.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" onclick=\"animc4bec7bf370947c88ccabfa08cfe9c79.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selectc4bec7bf370947c88ccabfa08cfe9c79\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_c4bec7bf370947c88ccabfa08cfe9c79\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_c4bec7bf370947c88ccabfa08cfe9c79\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_c4bec7bf370947c88ccabfa08cfe9c79\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_c4bec7bf370947c88ccabfa08cfe9c79\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_c4bec7bf370947c88ccabfa08cfe9c79\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_c4bec7bf370947c88ccabfa08cfe9c79\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_imgc4bec7bf370947c88ccabfa08cfe9c79\";\n",
       "    var slider_id = \"_anim_sliderc4bec7bf370947c88ccabfa08cfe9c79\";\n",
       "    var loop_select_id = \"_anim_loop_selectc4bec7bf370947c88ccabfa08cfe9c79\";\n",
       "    var frames = new Array(12);\n",
       "    \n",
       "  frames[0] = \"\\\n",
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       "m7UAAAAASUVORK5CYII=\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        animc4bec7bf370947c88ccabfa08cfe9c79 = new Animation(frames, img_id, slider_id, 800.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#双指针正负交叉排序可视化\n",
    "visualize_pointer_movement_with_squares(test_nums, algorithm2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img1e6b7d2c98984876832c4759127985b1\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider1e6b7d2c98984876832c4759127985b1\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim1e6b7d2c98984876832c4759127985b1.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" onclick=\"anim1e6b7d2c98984876832c4759127985b1.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" onclick=\"anim1e6b7d2c98984876832c4759127985b1.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" onclick=\"anim1e6b7d2c98984876832c4759127985b1.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" onclick=\"anim1e6b7d2c98984876832c4759127985b1.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" onclick=\"anim1e6b7d2c98984876832c4759127985b1.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" onclick=\"anim1e6b7d2c98984876832c4759127985b1.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" onclick=\"anim1e6b7d2c98984876832c4759127985b1.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" onclick=\"anim1e6b7d2c98984876832c4759127985b1.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" onclick=\"anim1e6b7d2c98984876832c4759127985b1.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select1e6b7d2c98984876832c4759127985b1\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_1e6b7d2c98984876832c4759127985b1\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_1e6b7d2c98984876832c4759127985b1\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_1e6b7d2c98984876832c4759127985b1\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_1e6b7d2c98984876832c4759127985b1\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_1e6b7d2c98984876832c4759127985b1\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_1e6b7d2c98984876832c4759127985b1\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img1e6b7d2c98984876832c4759127985b1\";\n",
       "    var slider_id = \"_anim_slider1e6b7d2c98984876832c4759127985b1\";\n",
       "    var loop_select_id = \"_anim_loop_select1e6b7d2c98984876832c4759127985b1\";\n",
       "    var frames = new Array(12);\n",
       "    \n",
       "  frames[0] = \"\\\n",
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       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim1e6b7d2c98984876832c4759127985b1 = new Animation(frames, img_id, slider_id, 800.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#双指针可视化\n",
    "visualize_pointer_movement_with_squares(test_nums, algorithm3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#时间复杂度对比——O（nlogn）vs O（n）\n",
    "import time\n",
    "import random\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_data(length_nums, n):\n",
    "    nums = list(range(-length_nums, length_nums))\n",
    "    select_nums = random.sample(nums, n)\n",
    "    new_nums = [element for element in nums if element not in select_nums]\n",
    "    return new_nums"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-20, -16, -15, -14, -12, -10, -8, -5, -3, 0, 1, 2, 3, 5, 6, 7, 9, 12, 14, 18]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "generate_data(20, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#序列长度\n",
    "start_length_nums =10\n",
    "end_length_nums =1001\n",
    "length_nums = list(range(start_length_nums, end_length_nums, 10))\n",
    "len(length_nums)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#运行时间计算函数\n",
    "def measure(algorithm, length_nums):\n",
    "    trial_nums = 20    #每个序列长度测试trail_nums次，算平均运行时间\n",
    "    time_list = []\n",
    "    for length in length_nums:\n",
    "        nums = generate_data(length,length)\n",
    "        total_time = 0\n",
    "        for _ in range(trial_nums):\n",
    "            start_time = time.perf_counter() \n",
    "            algorithm(nums)\n",
    "            end_time = time.perf_counter() \n",
    "            total_time += end_time - start_time\n",
    "        avg_time = total_time / trial_nums\n",
    "        time_list.append(avg_time)\n",
    "    return time_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#时间复杂度O（nlogn）\n",
    "o_nlog = [(num*math.log(num,200))/1000000 for num in length_nums]\n",
    "#时间复杂度O（n）\n",
    "o_n = [0.6*num/1000000 for num in length_nums]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制时间复杂度图\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.plot(length_nums, measure(algorithm1, length_nums), label='Algorithm 1 - Time')\n",
    "plt.plot(length_nums, measure(algorithm2, length_nums), label='Algorithm 2 - Time')\n",
    "plt.plot(length_nums, measure(algorithm3, length_nums), label='Algorithm 3 - Time')\n",
    "plt.plot(length_nums, o_nlog, label='O(nlogn)')\n",
    "plt.plot(length_nums, o_n, label='O(n)')\n",
    "plt.xlabel('Sequence Length')\n",
    "plt.ylabel('Time (seconds)')\n",
    "plt.title('Time Complexity')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
